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A nice discussion of implementing Heron's formula for the area of a triangle and avoiding numerical inaccuracies:

Def. If the difference between \(a\) and \(b\) is a multiple of a marsupial, then we say \(a\) and \(b\) are kangarooent.

The conjecture is: The Möbius Ladder on (2n) vertices always has one more spanning unicyclic subgraph than the Prism Graph on the same (2n) vertices.

I want to believe they match up in some way except the Möbius Ladder has one special one that doesn't make sense on the prism... and I can even guess that the "odd one out" for the Möbius Ladder is a a single cycle through all the vertices like the boundary of the Möbius band, but I don't see how to pair the rest up nicely.

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A "spanning unicyclic subgraph" is a subgraph which has a unique cycle, probably best thought of as "a spanning tree plus one more edge."

(Bear with me, the fun part is coming up.)

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I have a graph theory observation/conjecture which seems like it should be easy. Maybe someone will see it right away; I messed around for a depressing amount of time without success.

We'll need to know what a Prism Graph and a Möbius Ladder Graph are.

A video animating 99 different unexpected intersection points in various geometric configurations. Probably best viewed with your favorite musical background accompaniment; I suggest a piano trio by Haydn.

While this isn't quite what @christianp asked for in his recent post, it's still pretty enough in its own way.

Quick proof of a popular summation formula: Let S = {1,2,...,n}.
(1) How many ordered pairs (a,b) in the Cartesian product \(S\times S\)?
(2) For each \(k\in S\), how many of those ordered pairs have \(\max(a,b) = k\)?

The MAA maintains a list of recommendations for library holdings in mathematics:

Does anyone know of a similar resource for computer science?

It's a bit tedious, but you can show by induction that the n-th partial sum is (n⁴ + lower degree terms)/(96n⁴ + lower degree terms).

Has anyone figured out yet whether Snaky is a winner or loser in generalized ticktacktoe? It looks like the question is still open, but if anyone has any definitive sources...

Good Saturday morning calculus challenge: Evaluate \[\sum_{n=1}^\infty \frac{\cos(n)}{n}\] and \[\sum_{n=1}^\infty \frac{\sin(n)}{n}\] in exact terms.

Does anyone know any modern 3-player games (probably card or board games) that use Skat's characteristic structure, where the strongest player, determined by bidding, must defeat the cooperative play of the other two?

(perhaps the best tip comes from mst3k: I should really just relax.)

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After $bigint years, I *still* find it difficult to make a good 2-hour final for a calculus class. I think I end up with decent ones, but I spend unconscionable amounts of time designing, balancing, trimming, simplifying, ordering, usf, usw.

I took a look around to see what tips & tricks I could steal for composing good calculus tests, and there's either very little on the web, or it's just too hard to find because it's buried by tips on *taking* (mostly standardized) calculus tests.

More Substantial Hint 

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Puzzle problem: Suppose \(A_1, A_2, \ldots, A_n\) are finite sets, and each \(A_i\) contains an odd number of elements. Prove that there is a set \(S\subseteq \left\{1, 2, \ldots, n\right\}\) such that \(\displaystyle\sum_{i\in S} \left|A_i \cap A_j\right|\) is odd for every \(j\in \left\{1, 2, \ldots, n\right\}\).

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